In many control system applications it is desirable to modify multiple inputs to achieve a desired output characteristic. In systems with a large number of inputs, the control system becomes overly complex.
An example of such a system is coherently beam combined fiber laser arrays being operated in a high vibration environment. Coherent beam combining (CBC) generally requires that the lasers' phases be locked together using a closed-loop servo controller. For optimal packaging, it is advantageous for the controller to lock all the laser channels using only a single optical sample of the combined beam, i.e. to generate a multiplicity of error signals from a single physical measurement. Such multi-channel phase-locking controllers are limited in their scalability to high control speeds and channel counts by the limited information content of a single beam sample. In general, there is a finite trade space for controller speed (bandwidth) against channel count scalability.
Past CBC development work has sought to develop multi-channel phase-locking controllers scalable to large channel count. To maximize channel count scalability, such controller designs are typically optimized for modest control bandwidths focused on removing internal phase noise that is typically dominated by internal coolant flows, generally with low amplitude. However, when fiber amplifiers are operated in vibrationally noisy environments such as on moving air or ground platforms, the internal phase noise can be overshadowed by platform-induced vibrational phase noise. For example, in an environment having 2.4 g random vibration, acoustic frequency (<˜10 kHz) phase noise may be on the order of >100's of radians (rad) RMS with RMS phase noise slews (angular frequency shifts) of 600 krad/s, and peak slews of >2 Mrad/s. This is >100× the internal phase noise, and it is well beyond the demonstrated ˜few 10s of krad/s controller bandwidth of existing phase-locking controllers such as Locking of Optical Coherence by Single-detector Electronic Frequency Tagging (LOCSET) and Stochastic Parallel Gradient Descent (SPGD).
LOCSET uses multi-frequency dither techniques. In these methods, a small (<<1 radian) phase dither tag is applied at a unique frequency on each laser channel. When the mutually coherent beams are geometrically combined with each other, the resulting interference creates beating in the time domain at the superposition of tagging frequencies. Coherent detection methods can be used to isolate the beat phase at each frequency, and use this as an error signal for feedback control of each channel's phase. As the number of channels in the array is increased, more RF bandwidth is required to accommodate the unique dither frequencies for the new channels. Hence, ultimate scaling is limited by signal-to-noise, since upon adding channels the signal-to-noise of any individual channel's unique dither frequency modulation amplitude is decreased relative to the larger DC background of the combined beam's power and thus indirectly results in a trade of channel count against bandwidth as more averaging is eventually required to recover a measurement associated with a particular channel. LOCSET suffers from the disadvantage of requiring unique frequency RF components for each laser channel.
SPGD is a model-independent controller method that, like LOCSET, has its origins in adaptive optics. It involves applying uncorrelated sets of dither vectors simultaneously (i.e., at the same clock rate) on all laser channels, and simply uses a hill climbing algorithm to maximize the detected power. When the power is maximized, all beams are in phase with one another. SPGD differs fundamentally from LOCSET in that SPGD does not directly detect the phases of each beam, but only maximizes an aggregate metric (the combined power) that depends on the individual phases. SPGD has generally been regarded as delivering inferior performance to LOCSET, both in terms of scaling to higher channels counts and in scaling to higher control bandwidths. Adding more laser channels effectively adds more dimensions to the multi-dimensional hill that needs to be climbed in phase space, so the convergence time increases proportionally to the channel count.